Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
624 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. #16839786 | C4 | semidirect |
| 19. #16839785 | C4 | semidirect |
| 20. #16839785 | C4 | semidirect |
| 21. C61×#423 | C4 | semidirect |
| 190. #423 | #6923 | semidirect |
| 194. C61 | #11245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462472 | 2 |
| #21461531 | 2 |
| D61⋊#338 | 2 |
| C2×#16840629 | 2 |
| #21454381 | 2 |
| #11245 | 61 |